Dec 30 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R6C2 can only be <9>
R4C2 can only be <1>
R4C6 can only be <3>
R7C2 can only be <8>
R5C1 can only be <6>
R5C9 can only be <9>
R5C4 can only be <1>
R5C5 can only be <2>
R5C6 can only be <4>
R1C2 is the only square in row 1 that can be <4>
R8C7 is the only square in row 8 that can be <4>
Squares R3C2 and R3C9 in row 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <37>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C1 - removing <7> from <789> leaving <89>
Squares R6C5 and R6C8 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <56>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C4 - removing <5> from <578> leaving <78>
Squares R4C8 and R6C8 in column 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <56>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C8 - removing <6> from <1268> leaving <128>
R7C8 - removing <5> from <159> leaving <19>
R9C8 - removing <6> from <12689> leaving <1289>
Intersection of row 9 with block 7. The values <37> only appears in one or more of squares R9C1, R9C2 and R9C3 of row 9. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain these values.
R8C1 - removing <7> from <12579> leaving <1259>
Intersection of block 2 with row 2. The value <8> only appears in one or more of squares R2C4, R2C5 and R2C6 of block 2. These squares are the ones that intersect with row 2. Thus, the other (non-intersecting) squares of row 2 cannot contain this value.
R2C1 - removing <8> from <589> leaving <59>
R2C7 - removing <8> from <689> leaving <69>
Squares R1C7<68>, R2C7<69> and R3C8<89> in block 3 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <689>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C8 - removing <8> from <128> leaving <12>
R1C9 - removing <6> from <1267> leaving <127>
R2C9 - removing <6> from <136> leaving <13>
R9C9 is the only square in column 9 that can be <6>
Squares R3C1 and R3C8 in row 3 and R7C1 and R7C8 in row 7 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in columns 1 and 8 can be removed.
R2C1 - removing <9> from <59> leaving <5>
R8C1 - removing <9> from <1259> leaving <125>
R9C1 - removing <9> from <1279> leaving <127>
R9C8 - removing <9> from <1289> leaving <128>
R2C4 can only be <8>
R1C3 can only be <6>
R2C6 can only be <1>
R6C4 can only be <7>
R2C9 can only be <3>
R8C6 can only be <7>
R1C5 can only be <5>
R3C9 can only be <7>
R3C2 can only be <3>
R6C6 can only be <8>
R8C4 can only be <9>
R8C3 can only be <5>
R4C4 can only be <5>
R9C5 can only be <1>
R1C7 can only be <8>
R2C3 can only be <9>
R6C5 can only be <6>
R1C1 can only be <7>
R9C7 can only be <9>
R3C8 can only be <9>
R2C7 can only be <6>
R9C3 can only be <3>
R3C1 can only be <8>
R9C2 can only be <7>
R7C8 can only be <1>
R4C8 can only be <6>
R4C5 can only be <9>
R6C8 can only be <5>
R7C1 can only be <9>
R7C9 can only be <5>
R1C8 can only be <2>
R8C9 can only be <2>
R8C1 can only be <1>
R1C9 can only be <1>
R9C8 can only be <8>
R9C1 can only be <2>
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